It is possible, it's not a myth and you don't need to spend money.  

With anything in life, the more you work at it, the better you will become. Watch movies, listen to songs, write letters, read books and newspapers... And try talking as much as you can.  You need to do this every day to achieve your goal.

Another thing we ( learners) have to fight in orden to get fluency in an foreing language is to lose the fear to make mistakes and  not worry too much about grammar rules, the important thing is to achieve communication

that and not be ashamed or embarrased 

some of us have a high sense of ridiculous that is needed to overcome

Don't bother. We (non-native speakers) will never be able to speak English fluently. It's a myth that was created for English teachers to make money. At the end we'll all end up speaking with terrible pronunciation, constantly thinking about grammar rules. 

To speak English fluently, you should take into account many aspects, such as vocabulary, grammar etc. If you want to improve your skills - it will be better if you chat with a native-speaker as much as possible, enlarging your vocabulary and improving your conversational style.

I wouldn't be as pessimistic as one of the previous commentators, because even if fluency in English for non-natives is really a myth, which is not in my view, such myths give learners a great motivation in achieving better results mastering foreign languages.
The point is that in order to be a success story we should always raise our standards and zealously maintain them.